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Class LinearOptimizationEngine

用於模擬及解決線性程式的引擎。以下範例會解決下列線性程式：

兩個變數 x 和 y：
0 ≤ x ≤ 10
0 ≤ y ≤ 5

限制：
0 ≤ 2 * x + 5 * y ≤ 10
0 ≤ 10 * x + 3 * y ≤ 20

目標：
盡量提高 x + y

const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc Add two variables, 0 <= x <= 10 and 0 <= y <= 5
engine.addVariable('x', 0, 10);
engine.addVariable('y', 0, 5);

// Create the constraint: 0 <= 2 * x + 5 * y <= 10
let constraint = engine.addConstraint(0, 10);
constraint.setCoefficient('x', 2);
constraint.setCoefficient('y', 5);

// Create the constraint: 0 <= 10 * x + 3 * y <= 20
constraint = engine.addConstraint(0, 20);
constraint.setCoefficient('x', 10);
constraint.setCoefficient('y', 3);

// Set the objective to be x + y
engine.setObjectiveCoefficient('x', 1);
engine.setObjectiveCoefficient('y', 1);

// Engine should maximize the objective
engine.setMaximization();

// Solve the linear program
const solution = engine.solve();
if (!solution.isValid()) {
  Logger.log(`No solution ${solution.getStatus()}`);
} else {
  Logger.log(`Value of x: ${solution.getVariableValue('x')}`);
  Logger.log(`Value of y: ${solution.getVariableValue('y')}`);
}

方法

方法	傳回類型	簡短說明
`addConstraint(lowerBound, upperBound)`	`LinearOptimizationConstraint`	在模型中新增線性限制。
`addConstraints(lowerBounds, upperBounds, variableNames, coefficients)`	`LinearOptimizationEngine`	將限制條件批次新增至模型。
`addVariable(name, lowerBound, upperBound)`	`LinearOptimizationEngine`	在模型中新增連續變數。
`addVariable(name, lowerBound, upperBound, type)`	`LinearOptimizationEngine`	在模型中新增變數。
`addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)`	`LinearOptimizationEngine`	在模型中新增變數。
`addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)`	`LinearOptimizationEngine`	將變數批次新增至模型。
`setMaximization()`	`LinearOptimizationEngine`	將最佳化方向設為最大化線性目標函式。
`setMinimization()`	`LinearOptimizationEngine`	將最佳化方向設為盡量減少線性目標函式。
`setObjectiveCoefficient(variableName, coefficient)`	`LinearOptimizationEngine`	設定線性目標函式中變數的係數。
`solve()`	`LinearOptimizationSolution`	以預設的 30 秒期限，解決目前的線性程式。
`solve(seconds)`	`LinearOptimizationSolution`	解開目前的線性程式。

內容詳盡的說明文件

`addConstraint(lowerBound, upperBound)`

在模型中新增線性限制。限制的上限和下限會在建立時定義。變數的係數會透過對 LinearOptimizationConstraint.setCoefficient(variableName, coefficient) 的呼叫來定義。

const engine = LinearOptimizationService.createEngine();

// Create a linear constraint with the bounds 0 and 10
const constraint = engine.addConstraint(0, 10);

// Create a variable so we can add it to the constraint
engine.addVariable('x', 0, 5);

// Set the coefficient of the variable in the constraint. The constraint is now:
// 0 <= 2 * x <= 5
constraint.setCoefficient('x', 2);

參數

名稱	類型	說明
`lowerBound`	`Number`	限制的下限
`upperBound`	`Number`	限制的上限

回攻員

LinearOptimizationConstraint：已建立的限制

`addConstraints(lowerBounds, upperBounds, variableNames, coefficients)`

將限制條件批次新增至模型。

const engine = LinearOptimizationService.createEngine();

// Add a boolean variable 'x' (integer >= 0 and <= 1) and a real (continuous >=
// 0 and <= 100) variable 'y'.
engine.addVariables(
    ['x', 'y'],
    [0, 0],
    [1, 100],
    [
      LinearOptimizationService.VariableType.INTEGER,
      LinearOptimizationService.VariableType.CONTINUOUS,
    ],
);

// Adds two constraints:
//   0 <= x + y <= 3
//   1 <= 10 * x - y <= 5
engine.addConstraints(
    [0.0, 1.0],
    [3.0, 5.0],
    [
      ['x', 'y'],
      ['x', 'y'],
    ],
    [
      [1, 1],
      [10, -1],
    ],
);

參數

名稱	類型	說明
`lowerBounds`	`Number[]`	限制的下限
`upperBounds`	`Number[]`	限制的上限
`variableNames`	`String[][]`	要設定係數的變數名稱
`coefficients`	`Number[][]`	設定的係數

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`addVariable(name, lowerBound, upperBound)`

在模型中新增連續變數。變數會透過其名稱參照。類型設為 VariableType.CONTINUOUS。

const engine = LinearOptimizationService.createEngine();
const constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER);

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

參數

名稱	類型	說明
`name`	`String`	變數的專屬名稱
`lowerBound`	`Number`	變數的下限
`upperBound`	`Number`	變數的上限

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`addVariable(name, lowerBound, upperBound, type)`

在模型中新增變數。變數會透過其名稱參照。

const engine = LinearOptimizationService.createEngine();
const constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER);

// Add a real (continuous) variable
engine.addVariable(
    'y',
    0,
    100,
    LinearOptimizationService.VariableType.CONTINUOUS,
);

參數

名稱	類型	說明
`name`	`String`	變數的專屬名稱
`lowerBound`	`Number`	變數的下限
`upperBound`	`Number`	變數的上限
`type`	`VariableType`	變數類型，可以是 `VariableType` 的其中一個

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)`

在模型中新增變數。變數會透過其名稱參照。

const engine = LinearOptimizationService.createEngine();
const constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable(
    'x',
    0,
    1,
    LinearOptimizationService.VariableType.INTEGER,
    2,
);
// The objective is now 2 * x.

// Add a real (continuous) variable
engine.addVariable(
    'y',
    0,
    100,
    LinearOptimizationService.VariableType.CONTINUOUS,
    -5,
);
// The objective is now 2 * x - 5 * y.

參數

名稱	類型	說明
`name`	`String`	變數的專屬名稱
`lowerBound`	`Number`	變數的下限
`upperBound`	`Number`	變數的上限
`type`	`VariableType`	變數類型，可以是 `VariableType` 的其中一個
`objectiveCoefficient`	`Number`	變數的目標係數

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)`

將變數批次新增至模型。變數會以名稱來指稱。

const engine = LinearOptimizationService.createEngine();

// Add a boolean variable 'x' (integer >= 0 and <= 1) and a real (continuous >=0
// and <= 100) variable 'y'.
engine.addVariables(
    ['x', 'y'],
    [0, 0],
    [1, 100],
    [
      LinearOptimizationService.VariableType.INTEGER,
      LinearOptimizationService.VariableType.CONTINUOUS,
    ],
);

參數

名稱	類型	說明
`names`	`String[]`	變數的專屬名稱
`lowerBounds`	`Number[]`	變數的下限
`upperBounds`	`Number[]`	變數的上限
`types`	`VariableType[]`	變數類型，可為 `VariableType` 的其中一種
`objectiveCoefficients`	`Number[]`	變數的目標係數

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`setMaximization()`

將最佳化方向設為最大化線性目標函式。

const engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

// We want to maximize.
engine.setMaximization();

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`setMinimization()`

將最佳化方向設為盡量減少線性目標函數。

const engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

// We want to minimize
engine.setMinimization();

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`setObjectiveCoefficient(variableName, coefficient)`

設定線性目標函式中變數的係數。

const engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

參數

名稱	類型	說明
`variableName`	`String`	要設定係數的變數名稱
`coefficient`	`Number`	目標函式中變數的係數

回攻員

LinearOptimizationEngine - 線性最佳化引擎

`solve()`

以預設的 30 秒期限，解決目前的線性程式。傳回所找到的解決方案。

const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve();
if (!solution.isValid()) {
  throw `No solution ${solution.getStatus()}`;
}
Logger.log(`Value of x: ${solution.getVariableValue('x')}`);

回攻員

LinearOptimizationSolution - 最佳化解決方案

`solve(seconds)`

解開目前的線性程式。傳回所找到的解決方案，以及是否為最佳解決方案。

const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve(300);
if (!solution.isValid()) {
  throw `No solution ${solution.getStatus()}`;
}
Logger.log(`Value of x: ${solution.getVariableValue('x')}`);

參數

名稱	類型	說明
`seconds`	`Number`	解決問題的期限 (以秒為單位)；期限上限為 300 秒

回攻員

LinearOptimizationSolution - 最佳化解決方案